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Atom and Nuclei
Bohr's Atomic Model Postulate 1 Postulate 2 Postulate 3 Bohr Radius Radius is directly proportional to the square of n . Velocity is inversely proportional to n . Energy of a Bohr Orbit The energy of nth Bohr orbit = 13.6 / n2 Energy is inversely proportional to square of n . Binding Energy Ionization Energy It is directly proportional to the square of Atomic Number . Hydrogen Spectrum Planck's Quantum Theory Einstein's Mass - Energy Equation E = mc2 1 amu = 931 MeV De Broglie Equation Mass Defect Nuclear Binding Energy N.B.E. = { ZMp +(A-Z)MN - Mo } c2 where A-Z is the number of neutrons . Z is the atomic number ; Radioactivity α particles β particles γ particles Radioactive Decay Law Nuclear Fission Nuclear Fussion Wavelength of Electron Nuclear Coulombic Barrier The force of repulsion between the nucleus and approaching α particle is called as Nuclear Coulombic Barrier . Repulsive Potential Energy = V = (Z1e)(Z2e) / d = (Z1Z2)e2 / d The Nucleus Nuclear Size r = r0A1/3 {where r = nuclear size , A = Atomic mass number} r0 = 1.4 x 10-15 m = 1.4 fm Nucleus Proton Ratio Nuclei with even number of protons and neutrons are abundantly found . Nuclei with even - odd combination are intermediately found . Nuclei with odd - odd combination are rare . Nuclear Stability The Nucleus Proton Ratio gives us an idea of the stability of a nucleus . As atomic Number increases , the N/P ratio increases . (This is because the more number of neutrons are added than protons .) All nuclei above atomic number 82 , are beyond stability belt and are radioactive . Radioactive Decay Radioactive Decay takes place in order to stabilize the nucleus . In the process the atom may gain or loss it's entities . α Emission It is equivalent to a Helium Atom . An α emission eliminates 4 amu and 2 Z from an atom . Almost all elements above atomic number 82 decay by α emission . It leads to the formation of isodiapher i.e. difference in number of Neutrons and Protons remains same . β Emission It is equivalent to conversion of a neutron to proton . Thus , A β emission adds 1 Z to an Atom . A neutron is converted into a proton by removal of negative charge from it . Elements having a very high N/P ratio and that lie above the stability belt , undergo β emission , as neutrons are converted into protons are added . Positron Emission It is equivalent to a particle having no mass but positive charge . This particle is called as a positron . It is actually the conversion of proton to neutron by removing it's positive charge . A positron emission or β+ emission eliminates 1 Z from the atom . Electron Capture (K Capture) It is equivalent to an electron from K shell . In this emission , an electron from K shell is captured by the nucleus . AS an effect , a proton is converted into a positron . Electron capture mostly occurs with Heavier elements . γ Emission It is equivalent to a neutron . γ Emission causes no change . Nuclear DisIntegration Rate of DIsintegration Rate of DIsintegration = - dN/dt Rate α N Rate = λ N Integrated Rate Law λ = 2.303/t log10 N0/N N0/N gives the ratio of number of atoms , or the ratio of number of moles . Simultaneous Decay Decay pf an equimolar binary mixture . 2.303 log10N1/N2 = (λ2 - λ1) t Half Life Period t1/2 = 0.693 / λ Also ; at any point ; N = 2-n N0 Average Life Period λ' = 1/λ = t1/2 / 0.693 = 1.44 t1/2 Radioactivity Unit The standard unit of radioactivity is Curie . Parallel Radioactive Disintegration Suppose a Nuclei A splits into nuclei X and Y , then λA = λX + λY Fractional Yield of X = λX / λA Fractional Yield of Y = λY / λA Successive Radioactive Disintegration Daughter Nuclei , formed by parent nuclei also undergoes disintegration . Suppose A forms B and B forms C with λ1 and λ2 as disintegration constants ; N1/N2 = (λ2 - λ1) / λ1 Secular Equilibrium N1 / N2 = λ2 / λ1 i.e. radioactivity is not affected through the half-lives Disequilibrium Category:Physics